I had limited Greek character in charge being asinine (7)
I believe the answer is:
idiotic
'asinine' is the definition.
(thesaurus)
'i had limited greek character in charge' is the wordplay.
'i had' becomes 'id' (I'd).
'limited' means to remove the last letter.
'greek character' becomes 'iota' (letter from the Greek alphabet).
'in charge' becomes 'ic'.
'iota' with its final letter removed is 'iot'.
'id'+'iot'+'ic'='IDIOTIC'
'being' acts as a link.
(Other definitions for idiotic that I've seen before include "Daft" , "Altogether nonsensical" , "Absurd, crackbrained" , "Inviting ridicule" , "without any point" .)